A294278 Numbers k such that omega(k) > omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m).

6, 10, 12, 15, 18, 22, 24, 26, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63, 66, 70, 72, 78, 80, 82, 84, 88, 90, 96, 100, 102, 105, 106, 108, 110, 112, 114, 120, 124, 126, 130, 132, 136, 138, 140, 148, 150, 154, 156, 162, 165, 166, 168, 170, 172, 174, 178, 180

Offset: 1

Author

Rémy Sigrist, Oct 26 2017

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 1/2 (Erdős, 1936). - Amiram Eldar, Sep 17 2024

Examples

			omega(1) = 0 < omega(2) = 1, hence 1 does not belong to this sequence.
omega(4) = 1 = omega(5) = 1, hence 4 does not belong to this sequence.
omega(6) = 2 > omega(7) = 1, hence 6 belongs to this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link.

Crossrefs

Cf. A001221, A006049, A294277.

Programs

Mathematica

Position[Differences[Array[PrimeNu, 200]], ?(# < 0 &)] // Flatten (* _Amiram Eldar, Sep 17 2024 *)

PARI

for (n=1, 180, if (omega(n) > omega(n+1), print1(n ", ")))